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The value of p, for which the equation x2 + y2 - 2px + 6y - 7 = 0 represents a circle of radius 5 units, is:1. ±42. ±33. ±24. ±1 |
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Answer» Correct Answer - Option 2 : ±3 Concept: The radius of the circle x2 + y2 + 2gx + 2fy + c = 0 is given by r2 = g2 + f2 - c.
Calculation: Comparing the given equation x2 + y2 - 2px + 6y - 7 = 0 with the general equation of the circle we get: g = -p, f = 3, c = -7 Using the relation r2 = g2 + f2 - c, we get: ⇒ 52 = (-p)2 + 32 - (-7) ⇒ 25 = p2 + 9 + 7 ⇒ p2 = 9 ⇒ p = ±3 |
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